BIT-G: A Zero-Free-Parameter Rotation Curve Formula Derived from Boundary Information Theory

Abstract We present BIT-G, a rotation curve formula derived from Boundary Information Theory (BIT) that fits 175 SPARC disk galaxies at a mean absolute fractional error (MAFE) of 5.78% with zero parameters adjusted to the data. The formula takes the form V^2(r) = V_bar^2 + beta * c * H0 * r_c * Lambda_i * (1 - exp(-r/r_c)), where r_c = x* * R_last, Lambda_i = sqrt(lambda_c - 1) * D^(lambda_c - 1), and all constants (x* = 0.616, lambda_c = 1.554, beta = 0.0225) derive from BIT fixed-point mathematics, not from galaxy fitting. D = V_obs^2(r_c) / V_bar^2(r_c) is an observable, making the equation self-consistent (transcendental) with no per-galaxy free parameter. We identify D as the core variable of BIT-G: the dark-matter mass discrepancy at the BIT coherence radius governs the rotation curve. A thermal interpretation follows: galaxies with D > 1 exhibit a cooling tendency (toward the BIT freeze state), while D = 1 marks the thermal balance point at beta = 0.0225.